The cultural part of the transmission happens when the child learns the song from the father.
The gene part of co-evolutionary relationship happens when the females mate only with the males who sing the song produced by males of their own species.
Explanation:
The gene is known to a heredity unit that is transferred from a parent to the child and the gene plays a major role in determining the characteristic of the child.
The gene-culture transmission of birdsong illustrates that the songbirds usually learn the songs from other birds of their gene.